What Are The Chances Of Getting 4 Of A Kind In Poker

 
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A casino has a promotion where you get a bonus for getting each of the different 4-of-a-kinds in video poker. For simplicity, I assume each 4 of a kind occurs with equal probability. How does one calculate the average number of 4-of-a-kinds one must get before one can expect to have received each of the 13 different kinds at least once? There are 624 possible hands including four of a kind; the probability of being dealt one in a five-card deal is C 13 1 C 4 4 ⋅ C 12 1 C 4 1 C 52 5 = 13 ⋅ 1 ⋅ 12 ⋅ 4 2,598,960 ≈ 0.024%. With C a b = (a b). Double that to get an 8% chance to hit the straight on the turn and multiply it by 4 to get a 16% chance to hit it by the river. The actual poker odds of hitting an inside straight on the turn and then by the river are 8.5% and 16.5% respectively. A straight flush is a hand that contains five cards of sequential rank, all of the same suit, such as Q ♥ J ♥ 10 ♥ 9 ♥ 8 ♥ (a 'queen-high straight flush'). It ranks below five of a kind and above four of a kind. Under high rules, an ace can rank either high (as in A ♥ K ♥ Q ♥ J ♥ 10 ♥, an ace-high straight flush) or low (as in 5 ♦ 4 ♦ 3 ♦ 2 ♦ A ♦, a five-high.

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One of the great features of video poker is the fact that the odds of each hand being dealt are the same on every machine (Games with 52 cards of course have different odds to those with 53). While the pays for the wins change the chances of getting the wins do not. Below we list the odds of many hands being dealt pat and the odds of winning on the draw for a 52 card game.

Initial Deal Odds

The table below shows the odds of getting any winning hand on the first five cards dealt on a game using 52 cards. Odds change if you are playing a game with an additional wild card such as Jokers Wild as there are 53 cards.

HandOddsHand Odds
Royal Flush 1 in 649740Straight : 1 in 255
Straight Flush : 1 in 72193Three of a Kind :1 in 47
Four of a Kind : 1 in 4165 Two Pairs :1 in 21
Full House : 1 in 694Pair J, Q, K or A 1 in 7.69
Flush : 1 in 509Any Pair 1 in 2.37

Odds On The Draw

As much as we would all like to see a pat hand dealt every time we hit the max bet button this is rarely the case. In reality less than 1% of hands played will result in you holding all five where over 60% of hands you will hold just two cards going into the draw. Knowing this lets look at some examples.
The table below shows the odds of getting a particular hand when holding one, two, three or four cards. Of course you have to be holding the right cards for the odds to be correct. For example for cards to a royal is made up of four suited cards in the 10 to Ace range. Four to a flush is four suited cards etc.
Royal Flush Draw
Hold 1 Hold 2 Hold 3 Hold 4
1 in 178,3651 in 16,215 1 in 1081 1 in 47
Straight Flush Draw *
Hold 1 Hold 2Hold 3 Hold 4
1 in 59,4551 in 8,1071 in 360 1 in 47
Four of a Kind Draw
Hold 1 Hold 2 Hold 3 Hold 4
1 in 3,4301 in 3601 in 23.24n/a
Full House Draw
Hold 1 Hold 2 Hold 3 Hold 4
1 in 619 1 in 98 1 in 16 n/a
Flush Draw
Hold 1 Hold 2 Hold 3 Hold 4
1 in 3611 in 991 in 26 1 in 5
* The straight flush section has several variations that can change the odds that are displayed. These are primarily and inside draw or an outside draw. For example if you have 5h, 6h, 7h, 8h there are two ways to make the straight flush - either a 4h or a 9h will do it. However if you have an inside draw you have for example 2d, 3d, 5d, 6d. In this case only one card can make the hand (4d).
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Chances of hitting, flopping and holding certain hands

These odds are a must know if you want to advance your game to a high level. For exact odds you can check out our poker hand odds calculator. We rounded the number to the nearest decimal for you.

You should know what beats what in poker before trying to apply these odds or playing like you see poker on tv and in commercials.

What are the chances of getting 4 of a kind in poker games

What Are The Chances Of Getting 4 Of A Kind In Poker Lingo

Scenarios – Chances of Having Certain HandsExamplesProbability
Chances of Being Dealt
Pair

6h 6d

6%

Suited Cards

Ah 10h

24%

Connecting Suits

2d 3d

4%

Aces or Kings

AA KK

.9%

Ace King

AhKs

1.2%

Ace King Suited

AhKh

.3%

An Ace

A3

16%

Cards Jacks or Higher not Paired

KJ

9%

Not Suited & Not Connected

9h 4s

.9%

Bad Beats
Bad Beat ex: Aces vs Kings heads upAA vs KK

.004%

Chances of Hitting on Flop
Pocket Pair Into A SetJJ into JJJ

8%

Pair Turning Into A Set On Turn

4%

Hitting Pair on Flop

32%

Flopping Four To Flush-You hold 6h7h-flop comes->Ah Kh 2s

11%

Chances of Board Coming All Same5h 5s 5d

.004%

Number of Players To Flop Odds
Situation – Chances someone hit top pair on board
5 players see flop

58%

4 players see flop

47%

3 player see flop

35%

2 player see flop

23%

After Flop – Chances of Making Hand
Making open straight – You hold 67 Flop comes 8,9,2

turn 10

34%

Two pair to full house – You- 47 Board 4,7,10 Turn –>

7

17%

Hitting A Gut Shot Straight

17%

Backdoor Flush – You have 1 spade – Board 2s4h8s

10s 7s

4%

Runner Runner Straight

1.5%

Hitting Either Gut Shot Straight or Backdoor Flush

21%

Pairing An Ace on Turn or River

13%

Before Any Cards Are Dealt – Chances of Getting
Royal Flush (All Spades)AKQJ10

.0002%

Straight Flush (Any same suits)56789

.0012%

Four of a Kind (Quads)5555K

.0239%

Full House (Boat)33322

.144%

Flush (all same suit) =>all hearts37K48

.19%

Straight34567

.35%

Three of a Kind555AK

2.11%

Two PairAAKK2

4.7%

One Pair77253

42%

Don’t catch anything2854K

50%

What Are The Chances Of Getting 4 Of A Kind In Poker Card Game

Why Poker Odds Matter

Why Odds Matter To any good Texas Holdem players these odds come naturally. They may not know the exact percentage but they instinctively know their odds. Referencing this table is a great way to understand your percentages if you are a new player or if you want to calculate your pot odds.

Kind

What Are The Chances Of Getting 4 Of A Kind In Poker Games

We developed what we believe are the best formulas for calculating pot odds that you will find on the internet. It is the same way the pros calculate their pot odds and we also simplified it for those of you who are not that good at math. Check out the Pot Odds section.